Pressure differentiator

ABSTRACT

An object of the invention is to provide a pressure differentiator capable of improving measurement accuracy.  
     The pressure differentiator of the invention includes an isothermal pressure vessel  1,  a narrow tube  3  for connecting an object to be measured to the inside of the vessel  1,  and a differential manometer  2  for calculating a differential pressure between the object and the inside of the vessel  1.  It is preferable that a flow through the narrow tube  3  during measurement is a laminar flow. The isothermal pressure vessel  1  is fitted with a temperature equalizing material. As the temperature equalizing material, thin metal wires may be used. When the pressure P s  to be measured within a vessel positioned below is changed, the pressure P c  within the isothermal pressure vessel  1  is changed, with a slight lag, through the narrow tube  3.  By measuring the differential pressure P j  (=P s −P c ) at that time, using a diaphragm-type pressure differentiator, the derivative value of the pressure P s  may be calculated.

TECHNICAL FIELD

This invention relates to a pressure differentiator.

BACKGROUND ART

In a pneumatic control system, it is necessary to measure an outputsignal of a possible high order, in order to perform an accurate andrapid control. To this end, when the pressure within a vessel is to becontrolled by a pneumatic servovalve, for example, an advancedderivative control (D-PI control) is often used, in which the pressurewithin the vessel is measured by a pressure sensor and a signal obtainedby differentiating an output signal from the sensor using adifferentiator is fed back as a minor loop.

Many methods in which a high-order signal is estimated by a low-ordersignal, as described above, have been suggested. However, it is idealthat an actual value of the high-order output signal may be directlymeasured by a sensor. This is because the estimation is not easy becauseof an affect of a sensor noise and, further, a derivative of thepressure cannot be correctly detected when a pressure change is toosmall and below the resolving power of the sensor.

In relation to a pressure differentiator, a method for measuring adifferential pressure has been suggested. (For example, see Ernest O.Doebelin. Measurement Systems, McGran-Hill, (1976).) In other words, asa method for directly measuring a derivative of the pressure, a methodfor detecting a differential pressure between two sections by using adiaphragm has been suggested. This method utilizes a phenomenon in whichthe displacement of the diaphragm becomes a first order lag system forthe pressure when pressurization of one of the sections is carried outthrough a capillary tube. This configuration has been used in analtimeter of an aircraft.

On the other hand, an isothermal pressure vessel has been developed.(For example, see K. Kawashima, T. Fujita, T. Kagawa: Measurement Methodof Flow Rate Using Pressure Change in Vessel, Journal of the Society ofInstrument and Control Engineers (SICE), Vol. 32, No. 11, 1485/1492,(1996); and K. Kawashima, T. Kagawa, T. Fujita: Instantaneous Flow RateMeasurement of Ideal Gases. Trans. ASME Journal of Dynamic Systems,Measurement and Control, Vol. 122, pp. 174-178, (2000).)

DISCLOSURE OF THE INVENTION

The above method using the diaphragm has a problem that a measurementaccuracy of the method is low and the method cannot be used formeasuring a steep pressure change.

An object of the present invention is to resolve such a problem and toprovide a pressure differentiator by which the measurement accuracy maybe improved.

A pressure differentiator according to the invention has a vessel, ahollow channel for connecting an object to be measured to the inside ofthe vessel, and a differential manometer for calculating a differentialpressure between the object and the vessel.

At this point, a flow through the hollow channel during measurement maybe a laminar flow. The vessel may be an isothermal pressure vessel. Thevessel may be filled up with a temperature equalizing material. Thinmetal wires may be used as the temperature equalizing material. Further,a diaphragm-type differential manometer may be used as the differentialmanometer.

This invention produces the following effects.

As the pressure differentiator of the invention has a vessel, a hollowchannel for connecting the inside of the vessel to the object to bemeasured, and a differential manometer for calculating the differentialpressure between the object and the vessel, the measurement accuracy maybe improved.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of a pressure differentiator proposed bythe invention.

FIG. 2 is a graph indicating the change of a waveform of the pressureP_(s) in a simulation.

FIG. 3 is a graph indicating a result of a simulation in which theproposed pressure differentiator and a pressure differentiator with anempty vessel are used.

FIG. 4 is a graph indicating a result of a simulation of the temperaturechange in the empty vessel.

FIG. 5 is a graph indicating the change of a waveform of the pressureP_(s) in an experiment.

FIG. 6 is a graph indicating an experimental result of the proposedpressure differentiator and indicating the simultaneous differentiationvalue of the pressure P_(s).

FIG. 7 is a graph indicating an experimental result of the pressuredifferentiator with the empty vessel and indicating the simultaneousdifferentiation value of the pressure P_(s).

FIG. 8 is a graph indicating an experimental result of the pressuredifferentiator with the empty vessel and indicating the simultaneousdifferentiation value of the pressure P_(s).

BEST MODE FOR CARRYING OUT THE INVENTION

A best mode for carrying out the invention in relation to a pressuredifferentiator is described below.

First, a configuration and a measurement principle of the pressuredifferentiator proposed by the invention are explained. Next, anefficiency of the pressure differentiator is inspected by a simulation.Further, by experiment, an output signal of the pressure differentiatoris compared to a derivative of pressure obtained by simultaneouslydifferentiating an output signal of a manometer. Finally, an advantageof the proposed pressure differentiator is inspected by comparing theoutput signal of the pressure differentiator with an output signalobtained by using an empty pressure vessel having no copper wiretherein.

Major notations used in the embodiment are listed below.

Major Notations

A_(h): heating area of wall surface of pressure vessel, [m³];

C_(p): specific heat of air at constant pressure, 1.004×10³ [J/(kg K)];

C_(v): specific heat of air at constant volume, 0.716×10³ [J/(kg K)];

dv: inner diameter of manufactured pressure vessel, [m];

G: mass flow, [kg/s];

G_(do): output gain of proposed sensor;

h_(u): heat transfer coefficient (when air flows into pressure vessel),[W/(m² K)];

h_(e): heat transfer coefficient (when air flows out from pressurevessel), [W/(m² K)];

H_(v): height of manufactured pressure vessel, [m];

k: proportionality coefficient between output signal P_(j) anddisplacement x₀ of diaphragm-type differential manometer, P_(j)/x₀[Pa/m];

L: length of narrow tube, [m];

P_(s): pressure of object to be measured, [Pa abs];

P_(c): pressure within pressure vessel, [Pa abs];

P_(j): output signal of diaphragm-type differential manometer, [Pa];

Q: volume flow at normal state, [m³/s];

R: gas constant of air, 287.03 [J/(kg K)];

r: radius of narrow tube, [m];

Re: Reynolds number;

st: sampling time, [s];

P_(do): output of proposed pressure differentiator;

T: time constant of pressure within pressure vessel, [s];

T_(c): cutoff cycle, [s];

T_(se): thermal equilibrium time constant, [s];

V: volume of pressure vessel, [m³];

W: mass of air in pressure vessel, [kg];

θ: temperature in pressure vessel, [K];

θ_(a): outside air temperature, 293.15 [K];

x₀: displacement of diaphragm of differential manometer, [m];

μ: viscosity, [Pa s];

ρ_(a): density of air at atmospheric pressure, [kg/m³];

κ: specific heat of air, 1.4

FIG. 1 is a schematic diagram of a pressure differentiator according tothe embodiment.

The pressure differentiator has a vessel, a hollow channel forconnecting the inside of the vessel to an object to be measured, and adifferential manometer for calculating a differential pressure betweenthe object and the vessel.

As the vessel, an isothermal pressure vessel 1 may be used. The vessel 1is filled up with a temperature equalizing material. As the material,thin metal wires may be used, for example.

As the thin metal wires, thin copper wires may be used, for example. Thethin metal wires are not limited to the copper wires. Thin iron,aluminum or stainless wires, cotton or nylon may be used. In otherwords, a fibrous material, having a diameter within a range of 10-50 μmand a thermal conductivity larger than 0.05 W/(m K), may be used.

A volume ratio of the temperature equalizing material relative to thevolume of the isothermal pressure vessel is preferably within a range of3-15%. When the volume ratio is equal to or larger than 3%, an almostisothermal change may be advantageously achieved. When the volume ratiois equal to or less than 15%, the pressure is equally distributed in thevessel, whereby it would not be a problem to measure the pressureanywhere in the vessel.

Preferably, the volume of the isothermal pressure vessel is within arange of 1.0×10⁻⁸-1.0×10⁻⁴ m³. When the volume is equal to or largerthan 1.0×10⁻⁸ m³, the vessel is easy to manufacture. When the volume isequal to or less than 1.0×10⁻⁴ m³, measurement with a fast-response maybe possible.

One available object to be measured by the pressure differentiator isair. The object to be measured is not limited to air. Any gas, such asnitrogen, hydrogen or carbon dioxide, is possible.

A narrow tube 3 is a hollow channel for communicating the object to bemeasured with the inside of the isothermal pressure vessel.

An inner radius of the narrow tube is preferably within a range of0.00001-0.001 m. When the radius is equal to or longer 0.00001 m, theconstitution of the pressure differentiator is advantageously simple.When the radius is equal to or less than 0.001 m, it is easy to form alaminar flow.

The length of the narrow tube is preferably within a range of 20-500 mm.When the length is equal to or longer than 20 mm, an effect of pressureloss in an entrance region may be advantageously reduced. When thelength is equal to or shorter than 500 mm, the pressure differentiatorwith a high-response may be obtained.

Preferably, a flow within the narrow tube during measurement is alaminar flow. This is because the pressure is proportional to the flowrate and the pressure differentiator according to the invention may beconstituted.

A differential manometer is used to calculate a differential pressurebetween the object to be measured and the inside of the pressure vessel.As the differential manometer, a diaphragm-type differential manometermay be used. The differential manometer is not limited to thediaphragm-type. Any differential manometer, such as one using a bellows,may be used.

In FIG. 1, when the pressure P_(s) to be measured within a vesselpositioned below is changed, the pressure P_(c) within the isothermalpressure vessel is changed, with a slight lag, through the narrow tube.By measuring the differential pressure P_(j) (=P_(s)−P_(c)) at thattime, using the diaphragm-type pressure differentiator, the derivativevalue of the pressure P_(s) may be calculated.

A measurement principle of the pressure differentiator of the embodimentis explained below.

Assuming that the flow within the narrow tube is the laminar flow,according to an energy equation and the Hagen-Poiseuille law¹⁾), arelational expression of the change of the supply pressure P_(s) and thedisplacement of the diaphragm may be represented below.

State Equation of GasP_(c)V=WRθ  (1)

By the total differentiation of the above state equation, an equationbelow is obtained. $\begin{matrix}{{{P_{c}\frac{\mathbb{d}V}{\mathbb{d}t}} + {\frac{\mathbb{d}P_{c}}{\mathbb{d}t}V}} = {{{GR}\quad\theta} + {{WR}\frac{\mathbb{d}\theta}{\mathbb{d}t}}}} & (2)\end{matrix}$

Assuming that the pressure is isovolumetrically and isothermallychanged, an equation below is true. $\begin{matrix}{G = {\frac{V}{R\quad\theta}\frac{\mathbb{d}P_{c}}{\mathbb{d}t}}} & (3)\end{matrix}$

This indicates that the value G may be calculated by differentiating thevalue P_(c) when an initial temperature θ in the vessel and the gasconstant R are previously known, in the case of the isothermal vessel inwhich the thin metal wires are fitted (See K. Kawashima, T. Kagawa, T.Fujita: Instantaneous Flow Rate Measurement of Ideal Gases. Trans. ASMEJournal of Dynamic Systems, Measurement and Control, Vol. 122, pp.174-178, (2000)). According to past studies, an empty vessel and anisothermal vessel, including thin metal wires each having the averagediameter of 25 μm and having the density of 310 kg/m³, have been usedfor an experiment in which air is charged or discharged. It has beenreported that when the changes of temperature in the vessels is comparedto each other, only several Kelvin has been changed in the isothermalvessel, although about 40 Kelvin has been changed in the empty vessel(See K. Kawashima, T. Kagawa, T. Fujita: Instantaneous Flow RateMeasurement of Ideal Gases. Trans. ASME Journal of Dynamic Systems,Measurement and Control, Vol. 122, pp. 174-178, (2000)). $\begin{matrix}{Q = {\frac{\pi\quad r^{4}}{8\quad\mu\quad L}\Delta\quad p\quad\left( {{{wherein}\quad{Re}} \leq 2000} \right)}} & (4)\end{matrix}$

By using an equation of Hagen-Poiseuille law¹⁾, as described above, thevolume flow Q into the vessel, through the narrow tube having the radiusr, is represented as below. $\begin{matrix}{Q = {\frac{\pi\quad r^{4}}{8\quad\mu\quad L}\left( {P_{s} - P_{c}} \right)}} & (5)\end{matrix}$

When the density of air at atmospheric pressure ρa (=1.205 [kg/m³]) andthe pressure P_(c) are taken into account, the mass flow G isrepresented as below. $\begin{matrix}{{G = {{\rho_{a}\frac{P_{c}}{P_{a}}Q} = {\frac{\rho_{a}P_{c}\pi\quad r^{4}}{P_{a}8\quad\mu\quad L}\left( {P_{s} - P_{c}} \right)}}}{r_{s} = \frac{P_{a}8\quad\mu\quad L}{\rho_{a}\pi\quad r^{4}}}} & (6)\end{matrix}$

At this point, when a value r_(s) as indicated above is set as aresistance coefficient of the flow in the tube, the equation (6) may berewritten as below. $\begin{matrix}{G = {\frac{P_{c}}{r_{s}}\left( {P_{s} - P_{c}} \right)}} & (7)\end{matrix}$

Further, regarding the displacement x₀ of the diaphragm, equations beloware true by using a spring constant k. $\begin{matrix}{\frac{X_{o}}{k} = {P_{j} = {P_{s} - P_{c}}}} & (8) \\{P_{c} = {P_{s} - P_{j}}} & (9)\end{matrix}$

By the equations (3), (7) and (8), an equation below is obtained.$\begin{matrix}{{{\frac{\mathbb{d}}{\mathbb{d}t}\left( {P_{s} - P_{j}} \right)} = {\frac{P_{c}P_{j}}{r_{s}}\frac{R\quad\theta}{V}}}{K = \frac{R\quad\theta}{r_{s}V}}} & (10)\end{matrix}$

At this point, when a value K is defined as represented above and anequation (10) is Laplace transformed, an equation below is true.sP _(s) −P _(s)(0)−sP _(j) +P _(j)(0)=KP _(j) P _(c)   (11)P _(j)(0)=0

When an equation as described above is sequentially transformed, anequation below is obtained. $\begin{matrix}{P_{j} = {\frac{\frac{1}{P_{c}K}}{1 + {\left( \frac{1}{P_{c}K} \right)s}} \cdot \left\{ {{sP}_{s} - {P_{s}(0)}} \right\}}} & (13)\end{matrix}$

An equation below is true.${{sP}_{s} - {P_{s}(0)}} = {\left( \frac{\mathbb{d}P_{s}}{\mathbb{d}t} \right)}$

Further, as the value P_(c)(t) may be measured by means of themanometer, by the correction using the value P_(c)(t), the output of thepressure differentiator of the invention is represented below. Due to anequation (14), it is understood that a first order lag relation isestablished between the output P_(j) of the pressure differentiator andthe supply pressure P_(s). $\begin{matrix}{P_{do} = {{P_{c}P_{j}} = {{\frac{\frac{1}{K}}{1 + {\left( \frac{1}{P_{c}K} \right)s}} \cdot}\left( \frac{\mathbb{d}P_{s}}{\mathbb{d}t} \right)}}} & (14)\end{matrix}$

Assuming that the inside of the vessel is isothermal, the value K isconstant. Therefore, the output gain of the pressure differentiator asrepresented below is also constant. $\begin{matrix}{G_{do} = {\frac{1}{K} = \frac{P_{a}8\quad\mu\quad{LV}}{\rho_{a}\pi\quad r^{4}R\quad\theta}}} & (15)\end{matrix}$

In a region in which P_(c)≧P_(a) is true, a time constant as representedbelow becomes smaller as the inside of vessel is pressurized. By anequation (16), it is necessary to reduce the length L of the narrow tubeand the volume V of the vessel as possible, in order to lower theresponse time constant. $\begin{matrix}{T = {\frac{1}{P_{c}K} = \frac{P_{a}8\quad\mu\quad L\quad V}{P_{c}\rho_{a}\pi\quad r^{4}R\quad\theta}}} & (16)\end{matrix}$

When the differential pressure is calculated by measuring the valuesP_(s) and P_(c) using respective sensors, without using the diaphragmdifferential manometer, the measurement is very difficult, because thedifferential pressure is too small and below the resolving power of themanometer.

A response simulation of the pressure differentiator of the embodimentis explained below.

A response of the pressure differentiator utilizing the principle of theisothermal pressure vessel is compared to a response of a sensor usedfor an empty vessel as the pressure vessel, by means of a simulation ofSIMULINK, in order to inspect a theoretical effectiveness of thepressure differentiator.

A theoretical equation used in the simulation is explained.

In the simulation, the mass flow G is calculated by the equation (6). Atotal differential formula of the state equation of gas in the pressurevessel is represented by the equation (3) in the case of the proposedpressure differentiator and by the equation (17) in the case of theempty vessel used as the pressure vessel. Also, when the empty vessel isused, an energy equation including heat transfer in relation to the wallsurface is represented by an equation (18-1) when charging air and by anequation (18-2) when discharging air. $\begin{matrix}{\frac{\mathbb{d}P_{c}}{\mathbb{d}t} = {{\frac{P_{c}}{\theta}\frac{\mathbb{d}\theta}{\mathbb{d}t}} + {\frac{R\quad\theta}{V}G}}} & (17)\end{matrix}$

when charging $\begin{matrix}{\frac{\mathbb{d}\theta}{\mathbb{d}t} = {\frac{R\quad\theta}{C_{v}P_{c}V}\left\lbrack {{G_{u}\left( {{C_{p}\theta_{a}} - {C_{v}\theta}} \right)} + {h_{u}{S_{h}\left( {\theta_{a} - \theta} \right)}}} \right\rbrack}} & \left( {18\text{-}1} \right)\end{matrix}$

when discharging $\begin{matrix}{\frac{\mathbb{d}\theta}{\mathbb{d}t} = {\frac{R\quad\theta}{C_{v}P_{c}V}\left\lbrack {{{RG}_{e}\theta} + {h_{u}{S_{h}\left( {\theta_{a} - \theta} \right)}}} \right\rbrack}} & \left( {18\text{-}2} \right)\end{matrix}$

Parameters and a procedure of the simulation is explained.

Values of the parameters used in the simulation are listed below:

-   -   V: 4×10⁻⁵ m³;    -   Shape of vessel: assumed as sphere shape having radius of 21.216        mm;    -   S_(h): 4πr₁ ²=0.56564 m²;    -   θ: assumed as an isothermal model and a non-isothermal model;    -   r: 0.00075 m;    -   L: 150 mm;    -   h_(u): 50 W/(m² K)²⁾;    -   h_(e): 40 W/(m² K)²⁾

In the simulation, an initial value of the value P_(s) is assumed to beequal to an atmospheric pressure (101.3 kPa). The pressure is raisedafter 1 second from the beginning of the simulation, according to awaveform of first order lag having a time constant T of 0.6 second and,then, the pressure is kept at a constant value. After that, i.e., after6 seconds from the beginning of the simulation, the pressure is returnedto the atmospheric pressure according to a waveform of first order laghaving a time constant T of 1 second. The maximum value of the supplypressure is 252 kPa.

The response time constant T of the pressure differentiator is obtainedas below, by assigning the above parameters into the equation (15).T=0.00862 s−0.003465 s

Theoretically, a response frequency of the pressure differentiator isequal to or larger than 100 Hz.

A waveform indicating of the change of the value P_(s) in the simulationis shown in FIG. 2.

A result of the simulation is explained below.

FIG. 3 indicates the result of the simulation in the case of theproposed pressure differentiator and in case that the empty vessel isused as the pressure vessel. As shown in FIG. 3, it is understood thatthe pressure follows a true value without lag when the proposed pressuredifferentiator is used, on the other hand, the response of pressuredelays when the empty vessel is used. Also, a simulation in which themaximum value of the value P_(s) is changed carried out. In the case ofthe empty vessel, as the temperature θ in the vessel is changed when thepressure in the vessel is changed, the output gain G_(do) of thedifferential pressure sensor is also changed. As a result, when themaximum value of the value P_(s) is changed, for example, an error ofthe derivative value from the true value becomes larger. On the otherhand, in the case that the isothermal pressure vessel is used, such atendency is not observed.

FIG. 4 shows a result of a simulation in which the temperature in theempty vessel is varied. As shown in FIG. 4, it can be seen that, whenthe empty vessel is used, the temperature θ in the vessel is variedbetween 275K and 310K. The output gain G_(do) of the sensor calculatedby using the equation (15) is between 825.77(θ=310K) and 930.87(θ=275K).Therefore, the output gain G_(do) may be varied within about 13%.

It can be understood that, from the result of FIG. 3, a phase lag occursin the case of the empty vessel. This is because that the derivativevalue of the pressure is calculated by a theoretical equation whichignores the temperature change actually caused in the empty vessel. Inother words, in the case of the empty vessel, a transfer function of theflow rate and the pressure change in the vessel when discharging may becalculated as below, by Laplace transform of the total differentialformula of the state equation (17) and the energy equation (18-2).$\begin{matrix}{G = {\frac{V}{R\quad\theta}\frac{{T_{se}s} + 1}{{\kappa\quad T_{se}s} + 1}\frac{\mathbb{d}P_{c}}{\mathbb{d}t}}} & (19)\end{matrix}$

wherein: $T_{se} = \frac{C_{v}W}{hs}$

The value T_(se) is so called a time constant of thermal equilibrium²⁾.By the equation (19), a phase lag system is represented between thepressure change and the flow rate. Therefore, in comparison with therelational equation (1) indicating the pressure change and the flow rateG in the case of the isothermal pressure vessel, the phase lag occurs inthe case of the empty vessel.

Due to the above simulation results, a theoretical effectiveness of theproposed pressure differentiator is indicated.

The manufacture and an experiment of the pressure differentiator aredescribed below.

The pressure differentiator was actually manufactured and an experimentin which a changeable waveform was applied to the pressure P_(s) wascarried out, in order to demonstrate the effectiveness of the pressuredifferentiator.

The specification of the manufactured pressure differentiator is below:

-   -   shape of pressure differentiator: cylindrical (diameter d_(v)=50        mm, height H_(v)=20 mm)        ${{V\text{:}\frac{\pi}{4}d_{v}^{2} \times H_{v}} = {3.927 \times 10^{- 5}m^{3}}};$    -   r: 0.00075 m;    -   L: length of narrow tube=150 mm;    -   pressure sensor for measuring P_(a) and P_(c): Omron E8EB10C;    -   diaphragm type pressure sensor for measuring P_(j):        self-produced;    -   temperature equalizing material: copper thin wires having weight        of 14.4 g, each having diameter of 25 μm (volume ratio 4.24%,        length 3391.4 m, heat transfer area 0.2664 m²)

The procedure of the experiment is described below.

First, the initial value of P_(s) was assumed to be an atmosphericpressure (101.3 kPa). After about two seconds from the beginning of theexperiment, the pressure P_(s) was raised by stepwisely applying inputcurrent to a three-port nozzle-flapper type servovalve and, then, thepressure was kept at a constant value. After seven seconds from thebeginning of the experiment, the pressure was returned to theatmospheric pressure.

As the servovalve, a patented P075-221 was used. This servovalve wasconstituted from a nozzle and a flapper and configured to control theflow rate from the nozzle by displacing the flapper. A sampling periodst of data by a personal computer (PC) was 0.01 s. A maximum value ofthe supply pressure was 252 kPa. FIG. 5 shows the waveform indicatingthe change of P_(s) in the experiment. In FIG. 5, the waveform of P_(s)generally represents a first order lag system in which the time constantT is approximately equal to 0.6 second. This result depended on thecharacteristic of the three-port nozzle-flapper type servovalve used inthe experiment³⁾.

In the experiments, experiments regarding three cases were carried outand results thereof were compared to each other. In the three cases; (1)the proposed pressure differentiator with the isothermal pressure vesselwas used, (2) a manometer for measuring P_(s) was used and asimultaneous differentiation of the measured P_(s) was performed, and(3) the pressure differentiator with the empty vessel was used.

In addition, an equation below was used for calculating a simultaneousdifferential value of the manometer. $\begin{matrix}{\begin{matrix}{\frac{\mathbb{d}{P_{s}\lbrack i\rbrack}}{\mathbb{d}t} = {{\frac{1 + {\exp\left( {{- {st}}/T_{c}} \right)}}{2T_{c}}\left( {{P_{s}\lbrack i\rbrack} - {P_{s}\left\lbrack {i - 1} \right\rbrack}} \right)} +}} \\{\frac{\mathbb{d}{P_{s}\left\lbrack {i - 1} \right\rbrack}}{\mathbb{d}t}{\exp\left( {{- {st}}/T_{c}} \right)}}\end{matrix}{wherein}{{st} = {{0.01s\quad{and}\quad T_{c}} = {0.01{s.}}}}} & (20)\end{matrix}$

The results of the above experiments are described below.

First, the comparison between the output of the pressure differentiatorand the simultaneous differential value is explained. FIG. 6 shows thecomparison between the results of cases (1) and (2). As shown in FIG. 6,it can be seen that the pressure differentiator of the invention couldfollow the change of the pressure without lag, in comparison to thesimultaneous differential value of P_(s) measured by the pressuresensor. The graph of case (1) appears to proceed somewhat at a quickerpace than the graph of case (2), while the raised or lowered pressurewas gradually returned. This is because, from a speculation by ameasurement result of the static characteristic of the diaphragm, thecharacteristic of the used diaphragm type differential manometer underpressure was not sufficient.

Next, the comparison between the case using the empty vessel and thesimultaneous differential value is explained. FIG. 7 shows thecomparison between the results of cases (2) and (3). The result of FIG.7 indicates the similar tendency to the simulation result of FIG. 3. Itcan be seen that, in case (3) in which the empty vessel was used as thepressure vessel, an output amplitude was somewhat smaller than that incase (2) and the phase of the amplitude delayed in comparison to that incase (2).

FIG. 8 is an enlarged diagram including a peak value of the pressure inFIG. 7. Apparent from FIG. 8, the peak value when the empty vessel wasused was 195 kPa/s, on the other hand, the peak value obtained bysimultaneous differentiation of P_(s) was 220 kPa/s. Obviously, thisdifference of 25 kPa/s between them was a significant difference.Further, time of the peak value in the case of the empty vessel wassomewhat delayed in comparison to that in case (2).

By the above results, the effectiveness of the pressure differentiatorwith the isothermal pressure vessel is confirmed.

The results are as below.

In the proposed pressure differentiator of the invention, thedifferential value of the pressure P_(s) to be measured could bemeasured, without delay of the phase, as well as the differentialpressure value obtained by simultaneous differentiation of the outputsignal of the manometer.

Further, from the result in which the output of the proposed pressuredifferentiator was compared to the output signal of the pressuredifferentiator with the empty vessel having no copper wire therein, theoutput gain in the latter case was decreased as the pressure inside thevessel was reduced and the phase delay occurred. On the other hand, sucha problem was not observed in the proposed pressure differentiator.

Therefore, according to the best mode for carrying out the presentinvention, the pressure differentiator includes a vessel, a hollowchannel for connecting an object to be measured to the inside of thevessel, and a differential manometer for calculating a differentialpressure between the object and the inside of the vessel. Therefore, anaccuracy of measurement may be improved.

As the pressure differentiator may directly and accurately measure thederivative value of the pressure, the pressure differentiator may beused for improving the performance of a pneumatic control system or anair-conditioning control system in a chemical laboratory. Further, thepressure differentiator is available for measuring an unsteady flow rateof air.

The derivative value [Pa/s] of the pressure corresponds to a jerk valueor a derivative value of an acceleration. Therefore, the derivativevalue is important for controlling the pneumatic system. As the valuemay be directly measured by the invention, the performance of thecontrol may be improved. This is also possible when an environmentalchange is to be measured.

The invention should not be limited to the above best mode and,therefore, it should be apparent that numerous modifications could bemade thereto, without departing from the basic concept and scope of theinvention.

CITED REFERENCES

1) K. Sudo, T. Hasegawa, M. Shirakashi: Dynamics of Fluid, CoronaPublishing Co., Ltd (1994)

2) T. Kagawa, M. Shimizu: Dimensionless Pressure Response ConsideringHeat Transfer of Pneumatic Resistor Capacitor System, Hydraulics andPneumatics, (1988)

3) M. Yasuda: Active Micro-vibratory Control by Pneumatic Pressure,Journal of the Japan Hydraulics and Pneumatics Society (JHPS), Vol. 31,No. 5, pp. 14-19, (2000)

1. A pressure differentiator, characterized in that the pressuredifferentiator comprises: a vessel; a hollow channel for connecting anobject to be measured to the inside of the vessel; and a differentialmanometer for calculating a differential pressure between the object andthe inside of the vessel.
 2. The pressure differentiator as set forth inclaim 1, characterized in that a flow through the hollow channel duringmeasurement is a laminar flow.
 3. The pressure differentiator as setforth in claim 1, characterized in that the vessel is an isothermalpressure vessel.
 4. The pressure differentiator as set forth in claim 3,characterized in that the vessel is fitted with a temperature equalizingmaterial.
 5. The pressure differentiator as set forth in claim 4,characterized in that the temperature equalizing material is thin metalwires.
 6. The pressure differentiator as set forth in claim 1,characterized in that the differential manometer is a diaphragm typedifferential manometer.